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GCF of 431/288, 657/704

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 431/288, 657/704 i.e 1/6336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 431/288, 657/704.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 431/288,657/704?

Given fractions are 431/288,657/704

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 431/288,657/704, numerators are 431,657

Denominators are 288,704

The GCF of 431,657 is 1 .

LCM of 288,704 is 6336.

The greatest common factor of 431/288,657/704 = [GCF of 431,657]/[LCM of 288,704]= 1/6336

Therefore, the GCF of 431/288,657/704 is 1/6336.

Greatest Common Factor of 431,657

To find the highest common factor of 431,657, we have to find the factors of both numbers and list the highest common factor.

The factors of 431 are 1, 431

The factors of 657 are 1, 3, 9, 73, 219, 657

The HCF of 431,657 is 1.

Lets's calculate GCF of 431,657

Greatest Common Factor (GCF) of 431,657 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 431,657 By Matching Biggest Common Factor Method

Greatest Common Factor of 431,657 By Matching Biggest Common Factor Method

Now, list down the factors of 431

:

1,431

Now, list down the factors of 657

:

1,3,9,73,219,657

Greatest Common Factor

We found the factors 431,657 . The biggest common factor number is the GCF number.
So the greatest common factor 431,657 is 1.

Lets's calculate LCM of 288,704

Lowest Common Multiple of 288,704 using Common Division

2 288, 704
2 144, 352
2 72, 176
2 36, 88
2 18, 44
9, 22

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 9 x 22 = 6336

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6336

Therefore, the GCF of Fractions 431/288,657/704 is 1/6336

Least Common Multiple of 288,704 with GCF Formula

Least Common Multiple of 288,704 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 288,704 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(288,704) = 32

common factors(in case of two or more numbers have common factors) = 1

GCF(288,704) x common factors =32 x 1 = 32

LCM(288,704) = ( 288 × 704 ) / 32

LCM(288,704) = 202752 / 32

LCM(288,704) = 6336


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FAQs on GCF of Fractions of 431/288, 657/704

1. What is the HCF of 431,657?

The HCF of 431,657 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 431/288, 657/704?

Answer: GCF of Numerators as per given numbers 431/288, 657/704 is

GCF of Numerators i.e. for 431,657 is 1

LCM of denominators i.e. for 288,704 is 6336.

Thus, GCF of Fractions is 1/6336.Finally, GCF of Fractions for 431/288, 657/704 is 1/6336.